How runaway stars boost galactic outflows
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MNRAS 000, 1–14 (2020) Preprint 4 May 2020 Compiled using MNRAS LATEX style file v3.0
How runaway stars boost galactic outflows
1
Eric P. Andersson1? , Oscar Agertz1 and Florent Renaud1
Department of Astronomy and Theoretical Physics, Lund Observatory, Box 43, SE-221 00 Lund, Sweden
Accepted XXX. Received YYY; in original form ZZZ
arXiv:2003.12297v2 [astro-ph.GA] 1 May 2020
ABSTRACT
Roughly ten per cent of OB stars are kicked out of their natal clusters before ending their
life as supernovae. These so-called runaway stars can travel hundreds of parsecs into the
low-density interstellar medium, where momentum and energy from stellar feedback is effi-
ciently deposited. In this work, we explore how this mechanism affects large-scale properties
of the galaxy, such as outflows. To do so we use a new model which treats OB stars and their
associated feedback processes on a star-by-star basis. With this model we compare two hydro-
dynamical simulations of Milky Way-like galaxies, one where we include runaways, and one
where we ignore them. Including runaway stars leads to twice as many supernovae explosions
in regions with gas densities ranging from 10−5 cm−3 to 10−3 cm−3 . This results in more ef-
ficient heating of the inter-arm regions, and drives strong galactic winds with mass loading
factors boosted by up to one order of magnitude. These outflows produce a more massive
and extended multi-phase circumgalactic medium, as well as a population of dense clouds in
the halo. Conversely, since less energy and momentum is released in the dense star forming
regions, the cold phase of the interstellar medium is less disturbed by feedback effects.
Key words: galaxies: evolution – galaxies: star formation – stars: massive
1 INTRODUCTION Keller et al. 2014; Simpson et al. 2015; Hopkins et al. 2018). This
effort has made it possible to model galactic outflows in a cosmo-
Λ-cold dark matter has been highly successful in explaining and
logical context as an emergent property of clustered star formation,
predicting a variety of observed properties, such as large scale
with simulations now matching a range of observed galaxy proper-
structure, halo clustering and galaxy scaling relations (Eisenstein
ties (e.g. Hopkins et al. 2014; Agertz & Kravtsov 2015, 2016), as
et al. 2005; Springel et al. 2005; Viel et al. 2008; Reid et al. 2010;
well as properties of the turbulent ISM and giant molecular clouds
Klypin et al. 2011; Komatsu et al. 2011; Somerville & Davé 2015).
(GMCs; Grisdale et al. 2017, 2018, 2019).
Nonetheless, this model has also encountered challenges related to
Adding to the success of stellar feedback models, simulations
the ‘baryon cycle’, i.e. how galaxies accrete and expel their gas.
of entire galaxies has improved significantly in the recent years
Galaxy formation is an inefficient process, with at most ∼ 1/3 of
with parsec, or even sub-parsec spatial resolution and mass reso-
the cosmological baryon fraction being turned into stars in galaxies
lution reaching a few solar masses enabling models to capture the
as massive as the Milky Way, and significantly less in dwarf galax-
dense, cold ISM (see, e.g., Renaud et al. 2013; Rosdahl et al. 2017;
ies (e.g. Behroozi et al. 2019). This notion has been notoriously
Wheeler et al. 2018; Agertz et al. 2020). State-of-the-art simula-
difficult to predict by numerical simulations of galaxy formation,
tions can now resolve most of the cooling radii of individual SN ex-
which historically have suffered from excessive gas cooling and
plosions which allows them to capture the build-up of momentum
loss of angular momentum, leading to simulated galaxies with lit-
during the Sedov-Taylor phase which is crucial for robustly mod-
tle in common with observations (for a review on this topic, see
elling SNe feedback (Kim & Ostriker 2015; Martizzi et al. 2015a).
Naab & Ostriker 2017).
Furthermore, recent numerical studies have reached high enough
Galactic outflows, driven by stellar feedback (Dekel & Silk
resolution for individual stars to be modelled in galaxy scale simu-
1986) and active galactic nuclei (Benson et al. 2003), are com-
lations (Hu et al. 2017; Wheeler et al. 2018; Su et al. 2018; Emerick
monly believed to be instrumental for solving these problems
et al. 2019; Lahén et al. 2019). We stress however that despite the
(Somerville & Davé 2015). In the past decades, many studies have
improvements in galaxy modelling in the past decade, (subgrid)
explored ways of numerically capturing the impact of stellar feed-
stellar feedback still operates at the resolution level, with its cou-
back processes on the interstellar medium (ISM), e.g. effects from
pling to the ISM not yet being fully understood (Ohlin et al. 2019).
supernovae (SNe) explosions, stellar winds, radiation from young
stars (see, e.g., Katz 1992; Stinson et al. 2006; Agertz et al. 2013; While the actual process of star formation is not yet captured
in galactic context, these simulations allow for star particles to rep-
resent individual stars, all sampled from an initial mass function
? E-mail: eric@astro.lu.se (IMF) with subsequent feedback processes emerging on a star-by-
© 2020 The Authors2 E. P. Andersson et al.
star basis rather than from macro particles representing entire stel- by Sormani et al. (2017). In a mass bin indexed by i, a number of
lar populations. However, while galaxy simulations have started to stars ni is determined through realisations of a Poisson distribution
resolve the stellar component star-by-star, they are still far from given by
treating the stars collisionally. While a collisionless approxima-
λ ni
tion is valid on galactic scales, star-star interactions drive the in- Pi (ni ) = i e−λi , (1)
ternal dynamics of dense star clusters. As a result, some fraction ni !
of OB stars are kicked out of their natal star clusters with veloci- where the mean of the distribution, λi , is given for each bin by
ties large enough to move them out of the dense star forming gas
M
before exploding as SNe (e.g., Gies & Bolton 1986; Gies 1987; λi = fi , (2)
Stone 1991; Hoogerwerf et al. 2000; Schilbach & Röser 2008; Jilin- mi
ski et al. 2010; Silva & Napiwotzki 2011; Maíz Apellániz et al. where for bin i, in which stars have an average mass of mi , there
2018). Simulation of clusters (e.g., Oh & Kroupa 2016) reveal is a fraction of mass fi out of the total mass M, available for star
that such velocity kicks originates from gravitational interactions formation. The total stellar mass generated in N bins is then
(Poveda et al. 1967), including the disruption of binaries through
N
SNe (Blaauw 1961). None of these effects can be taken into account Õ
Msampled = ni mi, (3)
self-consistently without collisional dynamics, which currently is
i=1
computationally infeasible in galaxy scale simulations.
Massive runaway stars have been suspected to impact galaxy which is approximately equal to the mass M, due to the stochas-
evolution through efficient injection of energy into low density gas tic sampling, but converges towards M for large numbers of stars.
(Naab & Ostriker 2017). Coupling energy from SNe to gas depends There are two properties of this method which makes it ideal for
both on the phase of the gas (Katz 1992; Ceverino & Klypin 2009), our simulations. Firstly, the computational expense is determined
as well as on the structure of the ISM (Kim & Ostriker 2015; Mar- by the number of adopted mass bins, since the method only samples
tizzi et al. 2015b; Walch & Naab 2015; Iffrig & Hennebelle 2015; one random number for each bin and not for every star. Secondly,
Ohlin et al. 2019). Because runaway stars move away from their the bin-sizes can be chosen arbitrarily, which allows for stars below
natal regions, SN energy from these objects ought to couple dif- a certain mass threshold to be grouped in a single bin, while stars
ferently compared to the stars which remains in closer proximity above this mass are sampled at high mass resolution.
to the dense star forming gas. Typically explosions in low density A problem with this method is the non-zero probability of
gas generate a hot bubble which expands and leaves the galaxy as sampling a population of stars with mass larger than the available
an outflow (Korpi et al. 1999; de Avillez 2000; de Avillez & Bre- gas mass. To avoid this, we sample the IMF starting from the low-
itschwerdt 2004; Joung & Mac Low 2006). A similar effect has also mass end until either reaching the most massive stars defined by
been studied by comparing feedback from SNe positioned at den- the mass bins or until the available gas is depleted. In the first case
sity peaks compared to random positioning (see e.g. Korpi et al. we return the extra mass to the gas parcel where it was initially col-
1999; de Avillez 2000; de Avillez & Breitschwerdt 2004, 2005; lected, while in the second case we remove the most massive stars
Joung & Mac Low 2006; Walch et al. 2015; Martizzi et al. 2016; such that the stellar mass formed does not exceed the initial gas
Girichidis et al. 2016; Gatto et al. 2017). Although these exper- mass. This results in an IMF which is slightly more bottom heavy
iments are idealised, targeting only a small patch of the galaxy, than the one originally targeted, which in principle could lead to
they demonstrate that feedback from randomly located SN tends to weaken stellar feedback. Nonetheless, this effect is negligible com-
drive stronger outflows compared to explosions in density peaks. pared to the uncertainties in the models for stellar feedback.
This potentially impact the way the host galaxy forms and evolves Our model uses of the three part IMF from Kroupa (2001),
across cosmic time. where the number of stars of mass m is given by
In this paper we present a new model for treating individual
ξ(m) = AC j m−α j for m j ≤ m < m j+1, (4)
stars, focusing on the effect of runaways. The model has been ap-
plied to simulations of an isolated disc galaxy with properties sim- where A is a normalisation factor and C j are constants that ensures
ilar to the Milky Way. We describe how we model individual stars continuity in the intersections given by C1 = 1, C2 = C1 m2α2 −α1
as well as our treatment of runaway stars in Section 2. The numer- and C3 = C2 m3α3 −α2 . The three different parts are split into mass
ical setup and results are described in Section 3 and 4 respectively, regimes given by m1 = 0.01 M , m2 = 0.08 M , m3 = 0.5 M
while we discuss their implications in Section 5. Finally we sum- and m4 = Mmax , with slopes α1 = 0.3, α2 = 1.3 and α3 = 2.3. The
marise in Section 6. normalisation is determined for stars with masses between Mmin =
0.01 M and Mmax = 120 M .
In this work we sample stars from the aforementioned IMF
2 STAR FORMATION AND STELLAR FEEDBACK at each star formation event. We divide stars into high mass stars
(HMS) and low mass stars (LMS). The HMS are defined to have
In order to probe the effects of runaway stars, we implement a stellar masses larger than 8 M , sampled up to 40 M using 100
new recipe for treating massive stars as individual particles which equisized bins (giving a mass resolution of ∼ 0.3 M ). We do not
evolves during the simulation. In this section we describe the include stars more massive than 40 M in our model. Such stars
method used for sampling stars from an IMF, how feedback via are both exceedingly rare and their short lifetimes means that the
winds and SNe is treated and how it chemically enriches the ISM. distance traveled by very massive runaway stars is short. However,
these are extremely luminous important sources of feedback, es-
pecially in regards to stellar winds. Our model for stellar winds
2.1 Sampling the initial mass function
(described in detail in Section 2.3) has a strong scaling with stel-
Treating massive stars as individual particles requires a method to lar mass, and including these most massive stars can result in too
sample stellar masses. To do this efficiently we employ the method strong early feedback. Furthermore, we assume core-collapse SNe
MNRAS 000, 1–14 (2020)Increased outflows with runaways 3
for all HMS, which is unrealistic for too massive stars. In the code, As a first approximation, one can naively compute the distance
all HMS are treated individual particles. Since we are interested in stars travel before exploding as SNe by multiplying their mean ve-
the effect of feedback from massive (> 8 M ) runaway stars, the locity with the average main-sequence life time in the appropriate
rest of the IMF, defining the LMS, are lumped together into a single mass range. Using the velocity distribution given by Equation 5 we
macro particle to reduce the computational cost. find that stars in the mass range 8 M to 40 M with Z = Z 1
travels roughly 350 pc before exploding as supernova. This simple
model does not take into account deceleration from the gravita-
2.2 Runaway stars tional field of the cluster from which it escapes, and is therefore
In the simulations, particles are treated in a collisionless manner. a upper limit on the travel distance. Nonetheless it is of the same
To simulate runaway stars, we give velocity kicks to all particles order of magnitude as more detailed studies (see e.g. Eldridge et al.
representing individual stars (i.e. ≥ 8 M ) at their formation. The 2011; Renzo et al. 2019). The distance is significant, being an order
collisional effects leading to kicks operate on spatial scales many of magnitude larger than the average size of star forming molecular
orders of magnitudes below the gravitational softening length of clouds in the Milky Way (e.g. Heyer et al. 2009), and of the same
our simulations, warranting a ‘sub-grid’ approach. order of magnitude as the scale height of the cold gas disc.
The method assumes kicks distributed isotropically with ve-
locities, v, sampled from a power-law distribution,
2.3 Stellar feedback
fv ∝ v −β, (5)
HMS particles are considered as individually evolving stars and we
where the β is a free parameter in our model. The value of β de- consider mass loss, enrichment, momentum- and energy-injection
pends on several factors. Dynamical scattering events which gen- from fast winds and core-collapse SNe. In massive stars (≥ 8 M ),
erate kicks typically involve the interaction between a hard binary radiation pressure is significant enough to push away their outer
and a third star. The frequency of such encounters will therefore envelopes, giving rise to strong stellar winds for their entire main-
not only depend on the relaxation time of the cluster, but must also sequence evolution (see, e.g., Willis & Garmany 1987; Cassinelli &
be sensitive to the binary fraction. Moreover, as mentioned earlier, Lamers 1987). For this work we employ a model with a mass-loss
the kicks can also originate from the disruption of binary system rate based on Dale & Bonnell (2008) given by
caused by the SNe of one of the two components. This corroborates
Mb 4 γ
that binary fraction is a important parameter of the distribution of MÛ = 10−5 Z M yr−1, (6)
velocities. Furthermore, these processes implies a delay between 30 M
the formation of a star and the time when it gets a kick. Because of where Mb is the birth mass of the star. The scaling to the metal-
the complexity of this problem, estimates of β typically demands licity2 was added to the mass-loss rate to account for the metal-
the use of N-body simulations (see, e.g., Eldridge et al. 2011; Perets licity dependence of the photon coupling to the stellar envelope,
& Šubr 2012; Oh & Kroupa 2016; Renzo et al. 2019), but estimates which drives the wind. The metallicity exponent γ has been shown
from observations also exists (e.g., Hoogerwerf et al. 2000, 2001). to range between 0.5 and 0.8, (Kudritzki et al. 1987; Vink et al.
Furthermore, Banerjee et al. (2012) found that the velocity distri- 2001; Mokiem et al. 2007; Vink 2011) and in this work we adopt
bution shows some dependence on the mass of the runaway stars, γ = 0.5. The velocity of the fast winds typically ranges be-
with more massive stars reaching higher velocities (in agreement tween 1000 km s−1 and 3000 km s−1 in the literature (see, e.g.,
with Oh & Kroupa 2016). Leitherer et al. 1992; Lamers & Cassinelli 1999). We use a value
In this work, we choose a value of β = 1.8 and normalise the vw = 1000 km s−1 for our model, and inject the wind into the sur-
distribution for values between 3 km s−1 and 385 km s−1 , which rounding gas as a continuous source of momentum during the star’s
we apply to all HMS particles at formation without adding any time main sequence life time.
delay. This leads to ∼ 14% stars with velocities > 30 km s−1 . This HMS stars explode as core-collapse SNe at the end of their
choice is motivated by model MS3UQ_SP in Oh & Kroupa (2016), main sequence. The main sequence lifetime, tMS , for a star given
corresponding to runaways from a clusters with a mass of 103.5 M its mass and metallicity Z (here expressed as the total mass fraction
and half mass radii of 0.3 pc. Early observations indicated val- in elements heavier than He). To determine tMS our model uses a
ues for the runaway fraction of 30% (Stone 1991), however this stellar age-mass-metallicity fit by Raiteri et al. (1996), who found
is large compared to more recent work. As noted by Maíz Apel-
lániz et al. 2018 (see also Silva & Napiwotzki 2011), the results log tMS = a0 (Z) + a1 (Z) log m + a2 (Z)(log m)2, (7)
of Stone overestimates this fraction. Maíz Apellániz et al. found
where the coefficients are given by
observational evidence that 10−12% of O stars and a few percent
of B stars are so called runaway stars with significant peculiar ve- a0 (Z) = 10.13 + 0.07547 log Z − 0.008084(log Z)2,
locities (> 30 km s−1 ) with respect to their natal environment (in a1 (Z) = −4.424 − 0.7939 log Z − 0.1187(log Z)2, (8)
agreement with models by Eldridge et al. 2011; Renzo et al. 2019). a2 (Z) = 1.262 + 0.3385 log Z + 0.05417(log Z)2 .
Furthermore, the sampled velocities applied to the stars will change
through gravitational forces acting on the stars throughout their Note that this gives very similar main sequence lifetimes compared
lifetime. This change depends on the local gravitational field and to the single-star evolution (SSE) formulae by Hurley et al. (2000).
the entire galactic potential for stars with long enough life times.
This sensitivity to environment, together with the difficulty of com- 1 in this work we adopt Z = 0.02.
paring the observed population of runaway stars to the un-evolved 2 We track iron (Fe) and oxygen (O) abundances separately, and advect
velocity distribution, make a simple universal model (e.g. Equa- them as passive scalars. To construct a total metal mass M Z to use for
tion 5) uncertain. The reader should be cautious of this and note feedback and cooling,via the metallicity Z = M Z /Mgas , we adopt M Z =
that the results we present could overestimate the effect of runaway 2.09MO + 1.06MFe according to the mixture of α (C, N, O, Ne, Mg, Si, S)
stars. and iron (Fe, Ni) group elements relevant for the sun (Asplund et al. 2009).
MNRAS 000, 1–14 (2020)4 E. P. Andersson et al.
When a star explodes we deposit 1051 erg of energy into the gas where SF is the star formation efficiency per free-fall time, ρg is
the cell gas density and tff = 3π/32Gρ is the local gas free-fall
p
at the location of the star particle. If the SNe cooling radius is not
resolved, hence the momentum built up during the Sedov-Taylor time (see Agertz et al. 2013, for details). For this work we adopt
phase is not captured self-consistently, we explicitly inject the mo- ρ? = 100 cm−3 and sample star particles with a mass resolution
mentum from this phase following the scheme by Kim & Ostriker of 500 M , from which we remove mass for the HMS sampling
(2015, see also Martizzi et al. 2015a). Our implementation is iden- at each star formation event. For the simulations considered here
tical to that of Agertz et al. (2015) and Rhodin et al. (2019) and we we use a constant SF = 5%. Observationally, the efficiency per
refer the reader to these works for more details. free-fall time averages 1% in Milky Way giant molecular clouds
For LMS particles we consider mass loss, enrichment, (GMCs) (Krumholz & Tan 2007), albeit with a large spread (Mur-
momentum- and energy-injection for type Ia SNe and asymptotic ray 2011; Lee et al. 2016).
giant branch (AGB) winds. Details of the scheme can be found in
Agertz et al. (2013), with the adopted Kroupa IMF (Equation 4)
truncated at at the LMS upper mass limit (8 M ).
4 RESULTS
We reemphasise that including runaway stars provides a means to
3 NUMERICAL SETUP relocate massive stars away from their dense formation sites before
they end their lives in SNe, and our goal here is to explore how this
We have implemented the method described above in the N-body + process affects the evolution of a Milky Way-mass spiral galaxy.
Adaptive Mesh Refinement (AMR) code RAMSES (Teyssier 2002). The two galaxies are evolved for 250 Myr, a time during
RAMSES treats stars and dark matter through collisionless dynam- which they both are actively star forming. In the first 80 Myr the
ics using the particle-mesh method (Hockney & Eastwood 1981; galaxies adjust to their initial conditions, and in the case of the
Klypin & Shandarin 1983), with the gravitational potential calcu- runaways simulation there is a suppression in star formation after
lated by solving the Poisson equation using the multi-grid method 120 Myr (approximately one orbital time at the disc scale radius).
(Guillet & Teyssier 2011) for all refinement levels. The fluid dy- After these 120 Myr both simulations has stable star formation rate.
namics of the gas is calculated using a second-order unsplit Go- In this work all results taken as averages over time exclude this
dunov method with an ideal mono-atomic gas with adiabatic in- early phase unless otherwise stated.
dex γ = 5/3. The code accounts for metallicity dependent cooling Figure 1 shows projections along the line of sight for lumi-
by using the tabulated cooling functions of Sutherland & Dopita nosity, gas density and temperature for the galaxies at time t =
(1993) for gas temperatures of 104−8.5 K, and rates from Rosen & 250 Myr. Focusing first on the luminosity of the two galaxies, we
Bregman (1995) for cooling down to lower temperatures. find qualitative agreement between the two simulations, although
We have carried out two simulations of an isolated star form- we highlight that the runaways simulation has more stars in the
ing galaxy: one where the high-mass single stars are initiated with inter-arm region as well as above and below the disc mid-plane.
the velocity kick from the velocity distribution given by Equation 5 This indicates that the effect of runaway stars is subtle in the lumi-
using β = 1.4 (referred to as runaways), and a control simulation nosity of the galaxy. However, the projected gas density and tem-
where high-mass single stars are not assigned any velocity kick (re- perature largely differ between the two cases. Here runaway stars
ferred to as no runaways) as in traditional galaxy simulations. give rise to large (∼ kpc), hot (T > 106 K) bubbles in the inter-arm
The initial conditions are those of the isolated disc galaxy regions, as well as more prominent outflows (as seen on the edge-
in the AGORA project (Kim et al. 2014, 2016), set up to approx- on views) compared to the no runaways model. In general, the
imate a Milky Way-like galaxy following the methods described gaseous halo is more structured with warm (T < 106 K) clouds
in Hernquist (1993) and Springel (2000). Briefly, the dark matter found far away from the disc (& 5 kpc) in the runaways simula-
halo has a concentration parameter c = 10 and virial circular ve- tion.
locity v200 = 150 km s−1 . This translates into a halo virial mass
M200 = 1.1 × 1012 M within R200 = 205 kpc. The total bary-
onic disc mass is Mdisc = 4.5 × 1010 M with 20% in gas. The 4.1 Star formation rates and ISM properties
initial stellar and gaseous components follow exponential surface
We next consider the star formation rate (SFR) of the two simu-
density profiles with scale lengths rd = 3.4 kpc and scale heights
lations, shown in the upper panel of Figure 2. Excluding the initial
h = 0.1rd . The bulge-to-disc mass ratio is 0.125. The bulge mass
transient, both simulations have similar SFR (8−9 M yr−1 ) for the
profile is that of Hernquist (1990) with scale-length 0.1rd . The halo
first 120 Myr, followed by a decrease to a SFR of 5 − 6 M yr−1 in
and stellar disc are represented by 106 particles each, and the bulge
the runaways simulation for the remaining time. This decrease is
consists of 105 particles.
linked to the depletion of cold (T < 104 K) gas, which is shown
The galaxies are simulated in a box with sides 600 kpc with
in the lower panel of Figure 2. The simulation with runaway stars
adaptive mesh refinement allowing for a minimum cell size of 9 pc.
features less mass in the cold phase at all times, which ultimately
The refinement strategy uses a quasi-Lagrangian approach which
leads to a decline in the SFR3 .
ensures a roughly constant number of particles (∼ 8) in each cell
During the period of high SFRs for both models (80 Myr <
which reduces discreteness effects (Romeo et al. 2008). Further-
t < 120 Myr), more cold gas disappears in the runaways simu-
more, the AMR scheme splits cells into 8 new cells, each with mass
lation compared to the no runaways simulation. Quantitatively,
mrefine = 4014 M , when their sum of stellar and gas mass exceeds
the total cold gas mass decreases at approximately 30 M yr−1
8 × mrefine . Star formation uses a standard procedure with the star
formation rate density in cells exceeding a density threshold, ρ?,
given by 3 We note however that many other factors e.g. the level of gas turbulence,
ρg local star formation efficiency, GMC mass function will play a role in set-
ρÛ? = SF for ρg > ρ?, (9) ting the global SFR.
tff
MNRAS 000, 1–14 (2020)Increased outflows with runaways 5
runaways no runaways runaways no runaways runaways no runaways runaw
2 0 2 4 4 2 0 2 4 6 8 0.0
log( [L pc 2]) log( [cm 3]) log(T [K])
Figure 1. Projections of the stellar luminosity, gas density and temperature for face-on view (top row) and edge-on view (bottom row) from the last output
of the simulations, i.e., after 250 Myr of evolution. The side of each panel is 24 kpc. For each quantity we show the simulation taking runaway stars into
consideration to the left, whereas the simulation ignoring these stars is shown to the right.
and 15 M yr−1 for runaways and no runaways respectively.
Since the SFR is similar in both simulations at this epoch (thus hav-
10.0 ing similar amounts of cold gas turning into stars), the runaways
SFR [M yr 1]
7.5 model must reduce the net gas mass more efficiently, either by re-
moving it from this cold phase or inhibit warm gas from cooling
5.0 more strongly compared to the no runaways model. To some ex-
tent both of these likely play a role. After 120 Myr, the cold gas
mass loss rate changes to 7 − 10 M yr−1 in both simulations,
2.5 with the runaways simulation now having less cold gas in to-
0.0 tal. For the runaways simulation this transition coincide with the
decrease in SFR. This implies that even at low SFR, more cold gas
Mg (T < 104 K) [109 M ]
8.0 runaways is lost per unit of stellar mass formed in the runaways simulation.
no runaways To understand why the model with runaway stars predicts a
7.0 more rapid removal of the cold ISM from the galaxy, we focus to
the runaway mechanism, namely the effect of relocating SNe pro-
6.0 genitors. Figure 3 shows the projected gas density for the cold ISM
(T < 104 K). We selected outputs where both simulations included
5.0 visible SN bubbles (t = 200 Myr). The propensity of feedback from
runaway stars to create large bubbles in the inter-arm regions is ev-
4.00 50 100 150 200 250
ident. For the runaways simulation there are young massive stars
present in the voids, whereas for the no runaways all massive
Time [Myr] stars overlap with the low mass star particles by design.
Initially, density contrasts are generated by stellar feedback
Figure 2. Top: Star formation rate as function of time for the simulations and large scale gravitational instabilities, some of which evolves
with and without runaway stars. We neglect the transient caused by the sim- into bubbles. A crucial difference is that with the inclusion of run-
ulation adjusting to initial conditions (grey region). Both simulations reach away stars, the bubbles are resupplied with SN progenitors which
a steady state after approximately 120 Myr, before which we see a quasi keep injecting energy and momentum into them even though actual
stable period with enhanced SFR (starting at ≈ 80 Myr). There is a sup- star formation is impossible in those regions. This repeated injec-
pression in star formation at 120 Myr in the model including runaway stars. tion gives rise to kpc-scale bubbles in the runaways model, and
Bottom: Total mass of the cold (< 104 K) gas as function of time for the as we will discuss later it leads to energy venting into the CGM.
simulations, measured in a cylinder with a radii of 15 kpc and a thickness Throughout the runaways simulation many such bubbles form,
of 2 kpc
albeit with seemingly random timing.
Quantitatively, we find a clear excess of SNe explosions in
gas with 10−5 cm−3 < ρ < 10−3 cm−3 when including runaways,
peaking at more than twice as many explosions at ρ ∼ 10−4 cm−3
MNRAS 000, 1–14 (2020)6 E. P. Andersson et al.
runaways no runaways
2.0
1.5
1.0
0.5
log( [cm 3])
0.0
0.5
1.0
1.5
10 kpc
2.0
Figure 3. Projection plots of density for gas with temperature < 104 K for the model with (left) and without (right) runaway stars. The zoom in regions (4.7 kpc
wide) show the positions of young (< 10 Myr, pre-SNe) star particles located within 50 pc of the mid-plane, with HMS particles in white and LMS particles in
red. By construction, the two types exactly overlap in the no runaways case. In the runaways simulation a few HMS have traveled to regions completely
void of < 104 K gas. These stars are likely to explode inside the bubble.
200
runaways runaways
Half-mass height (pc)
no runaways 109 no runaways
150
Mass (M )
100 108
50 107
0 5 10 15 106 1000 0 1000
Radius (kpc) z (pc)
Figure 4. Left: Half-mass height of the cold (< 104 K) gas mass as function of radius. Solid line shows the mean of all outputs and coloured areas show the
standard deviation. Right: Vertical profile of the gas mass in the runaways simulation (red) and the no runaways simulation (blue). The filled line show
the mean of all outputs and the coloured region is the standard deviation.
with respect to the no runaways case. This implies a direct in- tion of runaway stars cause large bubbles in the inter-arm gas, the
jection of energy in low density regions in contrast with the typical overall structure of the cold ISM is very similar in both simulations.
injection sites of SNe. This mechanism is visible in Figure 3, and In fact, runaway stars produce a slightly thinner disc. Furthermore,
the resulting heating is visible in the face-on projection of the gas the vertical velocity dispersion of the cold gas is σz ∼ 20 km s−1
temperature in Figure 1. Finally, we note that the no runaways at radius R = 5 kpc for both simulations, with a roughly linear de-
simulation features, not surprisingly, more SNe in gas with higher crease to ∼ 5 km s−1 at 10 kpc after which it flattens out. This is
density compared to the runaways simulation. in close agreement with observed HI kinematics in nearby spiral
Despite this seemingly violent impact on the cold ISM, the galaxies (Tamburro et al. 2009). Hence, while runaway stars drive
overall structure of the disc remains intact. To some degree, run- strong turbulence and creates large bubbles it does not strongly alter
away stars alleviate the dense star forming gas from part of the feed- the morphology of the cold disc. This allows for the co-existence
back. This is demonstrated in Figure 4 were we show the structure of thin galactic stellar discs and strong galactic outflows, an other-
of the cold gas in the disc. The left plot shows the vertical distance wise challenging aspect of galaxy models (e.g. Agertz et al. 2011;
from the mid-plane of the disc within which half of the cold gas Roškar et al. 2014).
mass is located as function of radius. In the right plot we show the In summary, runaway stars induce in more efficient coupling
gas mass as function of vertical distance z. Although the introduc- of feedback to diffuse gas. The more rapid depletion of the cold
MNRAS 000, 1–14 (2020)Increased outflows with runaways 7
60
runaways 1000
no runaways
M [M yr 1]
|vz| [km s 1]
40 750
500
20
250 runaways
no runaways
0 0
M
Mass loading factor
100 10
Ratio
5
10 2
00 20 40 60 80 100
|z| [kpc]
10 4 0 50 100 150 200 250
Time [Myr] Figure 6. Top: Mean vertical velocity of the gas as function of vertical
height, with warm gas (2 × 104 < T < 106 K) as solid lines and hot gas
(106 < T < 108 K) as dotted lines. Bottom: Ratio of outflow rates (green)
Figure 5. Top: Vertical gas outflow rate as function of time for the two mod- and mass loading factor (orange) between the two simulations (runaways
els, measured in cylinders of radius 12 kpc and thickness 2 kpc, centred on divided by no runaways) as function of vertical distance. To compute the
±5 kpc from the mid-plane. The grey region is neglected since the simula- outflow rates we used bin heights of 1 kpc for |z | < 10 kpc, 2.5 kpc for
tion is still adjusting to the initial conditions during this time. When measur- 10 kpc < |z | < 30 kpc and 5 kpc for |z | > 30 kpc in order to account for
ing h MÛ i at different heights we see a similar time profile but re-scaled, i.e. the decreasing resolution with increased vertical height. The lines shows the
both lines are shifted down by the same amount when measuring at larger mean of all simulation outputs ignoring the first 80 Myr.
height. The runaways simulation features epochs of very strong outflows
due to the production of large bubbles, which keeps growing due to injec-
tion of supernovae energy by runaway stars. Bottom: Mass loading factor mass loading factor, defined as
as function of time for the two models, computed by dividing the outflow
Û
h Mi
rate with the SFR, which quantifies the efficiency of the stellar feedback in η= . (10)
driving outflows. We show this for three different heights: 5 kpc with 2 kpc SFR
thickness, i.e., identical to top panel (thick lines); 50 kpc with 10 kpc thick- Since η is very sensitive to the height where it is measured, we show
ness (thin dashed line); 100 kpc with 20 kpc thickness (think dotted line). it for three different |z| corresponding to roughly 0.025, 0.25 and
The selected distances corresponds to roughly 0.025 R200 , 0.25 R200 and
0.5 times the virial radius of the galaxy. For a given model, η varies
0.5 R200 .
up to three orders of magnitude depending on where it is measured.
However, the ratio between the simulations is mostly independent
of where we measure it. We will return to this notion later as well in
ISM found above is then a result of more vigorous galactic outflows
this section, as compare our models to observations in Section 5.3.
which we quantify in the next section.
Focusing on the innermost measurement, we find that at
100 Myr, η reaches its maximum at ≈ 0.5 in the no runaways
simulation. With the stronger outflows measured in the runaway
4.2 Galactic outflows
model, combined with the reduced SFR, the mass loading factor
The top panel of Figure 5 shows the vertical outflow rate as a func- is significantly higher throughout the entire duration of the simu-
tion of time for both models. The rates are computed by summing lation, with periods of η reaching values of ∼ 5 − 10. As we dis-
cell-by-cell contributions in a cylindrical region with a radius of cuss further in Section 5.1, such an efficient wind driving implies a
12 kpc centred on the galaxy for 4 kpc < |z| < 6 kpc, considering markedly different long term evolution for the galaxy.
only gas flowing in the vertical direction away from the mid-plane. Higher outflow rates do not necessarily imply faster galactic
The galaxy with runaway stars features significantly stronger out- winds. In fact, in the runaways simulation we find that warm
flows at all times, and right after the onset of the galactic wind outflows (2 × 104 < T < 106 K) carry more mass but travel at
(t > 80 Myr) the mass loss rate is more than 10 times higher than a lower velocity (see solid line in bottom panel of Figure 6) than
without runaway stars. This strong outflows in the runaways sim- in the no runaways simulation. If the galactic winds were purely
ulation is likely linked to the reduction in cold gas mass, causing the momentum-driven, the outflow mass would depend on the wind ve-
reduced SFR. At 150 Myr this wind calms down, although it still re- locity as m ∝ 1/v. We measure the velocity to be less than twice
moves mass at roughly twice the rate of the no runaways model. as high in the runaways which then would imply an outflow
Furthermore, there are burst of outflows (the largest of which takes mass no more than twice as high. However, the strong outflows
place at 200 Myr) linked to runaway stars generating a number of in runaways yield ∼ 3 times more gas mass in the halo (as shown
large (> kpc) bubbles (apparent in the middle panel in Figure 1). in Section 4.3). Therefore, this feedback is not momentum-driven.
In the bottom panel of Figure 5 we present the evolution of the Conversely, in the case of purely energy-driven winds, one would
MNRAS 000, 1–14 (2020)8 E. P. Andersson et al.
expect m ∝ 1/v 2 , i.e. at most four times more in the runaways, (T < 2 × 104K) (2 × 104 < T < 106K) (106 < T < 108K)
which is compatible with our mass measurements.
In both models, vz increases with vertical distance, indicating 15
that outflowing gas is accelerated by the continuously shock heated
hot phase. Moreover, in contrast to no runaways, the runaways 10
simulation features epochs of vigorous winds, with bursts of fast
moving, hot (T > 106 K) gas originating from the large bubbles 5
runaways
described earlier.
z [kpc]
In the top panel of Figure 6 we compare the mean outflow 0
properties between the two models as function of vertical distance
after 120 Myr. Regardless of vertical distance from the disc, the 5
model accounting for runaway stars always features an increased
mass loss rate as well as mass loading factor. The impact of run- 10
away stars on winds is hence not restricted to a narrowly defined
region, but rather acts like a outflow strength ‘multiplier’ all the 15
way up to ≈ 100 kpc. If generic, we note that this effect could al-
low for a simple treatment of the effect of runaway stars in semi-
analytical models of galaxy formation (see e.g. Somerville & Davé 15
2015) or cosmological simulations with phenomenological treat-
ments of galactic winds (e.g. Vogelsberger et al. 2013). 10
5
no runaways
z [kpc]
0
4.3 Structure of gaseous halo 5
As already shown, runaway stars drive a strong galactic winds,
launching large quantities of gas out in the halo. Despite the ab- 10
sence of cosmic inflows in our simulations and low resolution
(∼ 100 pc) in the halo, the circumgalactic medium (CGM) pro- 15
duced by the outflows does play a crucial role in the long term evo-
lution of the galaxy, e.g. by determining the recycling of gas used
for star formation. Unless otherwise stated, we focus now on gas 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5
within 40 kpc of the galaxy centre from which we remove the disc log( /cm 3)
(±2 kpc vertically and 15 kpc radially).
Figure 7 shows the projected density shown for three differ-
ent temperature ranges. Runaway stars produce a CGM which is Figure 7. Projected density of gas in different temperature ranges (left
more extended with the presence of long gas filaments and small panel: molecular gas; middle panel: warm ionised gas; right panel: hot gas)
shown in panels with widths of 15 kpc in the edge-on view. In all three
clouds. The clouds rise from the disc and dissipate on timescales of
phases the outflows caused by the inclusion runaway stars provide a sig-
tens of Myrs, in agreement with models of lifetimes of high veloc-
nificantly larger vertical scale. When comparing the time evolution of the
ity clouds around the Milky Way (Heitsch & Putman 2009). In our two simulations in this view, we find repeated large bubbles (most clearly
runaways simulation the motion of the clouds varies with some seen here in the hot gas) in the runaways simulation. These are absent in
clouds being accreted back onto the disc, some buoyantly floating the no runaways simulation. The snapshot shown here is the last output
above the plane and some lifted outwards until dissipation. The fil- (250 Myr).
aments are the result of ram pressure exerted on these clouds by the
hot medium.
At t = 250 Myr the gas mass in the considered halo re- 5 DISCUSSION
gion is 9.0 × 108 M and 2.9 × 108 M in the runaways
5.1 Implications for long term galactic evolution
and no runaways models respectively. The excess mass in the
runaways model is in very hot (> 106 K), low density (< We have demonstrated that simulations incorporating massive run-
10−2 cm−3 ) gas, shown in the contours of Figure 8 (as well as the away stars feature galactic outflows with higher mass loading fac-
histograms). The background colour of this plot gives the mass ra- tors compared to models without. This leads to a more massive and
tio between runaways and no runaways in different phases, structured galactic halo, and an overall reduction of the mass in the
where we see that the runaways model gives over one order of cold ISM.
magnitude more gas mass in this phase, demonstrating the more The star forming ISM is not only regulated more efficiently
efficient coupling of SNe energy to the halo. by galactic outflows, some fraction of the runaway stars travel far
In the density histogram of Figure 8 we also see more mass for enough to deposit energy into the inter-arm regions and the in-
ρ ≈ 1 cm−3 in the runaways model. This is gas with temperature ner galactic halo. This increases the thermal energy in diffuse gas,
∼ 104 K which sits in clouds and the filamentary structures. Finally, which in turn reduces the gas accretion rate of the galaxy and thus
we note that in the no runaways simulation there is more diffuse acts as a preventive feedback. Such a process is energetically more
(ρ ∼ 10−5 cm−3 ) gas in the range 105 < T < 107 K than in the efficient than mechanically ejecting the same amount of gas from
runaways simulation. the ISM. This means that stellar feedback with runaway stars does
MNRAS 000, 1–14 (2020)Increased outflows with runaways 9
105 101
M [M ]
103
10
Ratio (runaway/no runaway)
9
8
7 100
log(T [K])
6
5
4
3
2
1 10 1
6 4 2 0 103 105
log( [cm 3]) M [M ]
Figure 8. Comparison between the runaways (red) and no runaways (blue), as seen in the phase of the halo gas at the end of the simulation. The lines
shows the mass distribution in gas phase, where contours are given for 1%, 10%, 40% and 80% and histograms shows the sum of all values along a given
axis value. The background map shows the ratio between the models, coloured such that red indicated excess in runaways and blue indicated excess in
no runaways.
not only lead to increased mass loading factors in galactic winds, Early works studied SNe placement based on density thresholds
but that it also includes a higher energy deposition into halo gas (Li (Korpi et al. 1999) and showed that some SN explosions must oc-
& Bryan 2019). cur in isolation in order to produce a realistic multi-phase ISM (see,
Although our simulations have only been carried out for 250 e.g., de Avillez 2000; de Avillez & Breitschwerdt 2004; Joung &
Myr due to the high computational cost associated with treatment Mac Low 2006; Walch et al. 2015; Li et al. 2017). In agreement
of individual stars, the above mechanisms imply a more efficient with our results, these authors have found an increased effect from
regulation of star formation over Gyr timescales, and hence an stellar feedback as a result of randomly placed SNe. In fact, models
overall impact on galaxy evolution over a Hubble time. Applying with stellar feedback injected over a broad range of densities leads
our model in fully cosmological simulations, even for a limited to a very turbulent ISM and an overall reduction of star formation.
amount of time, would be of great interest for shedding light on Additionally, Kim & Ostriker (2018) found an increased mass load-
how runaway stars affect earlier phases of galaxy formation (z > 1) ing factor as a result of including runaway stars, especially for hot
when gas accretion rates are significantly higher than at the current gas, although this depends quantitatively on the vertical structure
epoch and efficient stellar feedback is know to be important (e.g. of the disc (Li et al. 2017).
Agertz & Kravtsov 2016). Runway star physics may therefore aid The volume filling factor of gas with different temperatures
in explaining the inefficiency of galaxy formation from e.g. abun- has, not surprisingly, been shown to be affected by randomly placed
dance matching (Behroozi et al. 2019), and will impact the pre- SNe (see, e.g., de Avillez & Breitschwerdt 2004; Walch et al. 2015).
cise galaxy mass range over which AGN feedback dominates stel- This is also the case in our work, with more of the volume filled by
lar feedback (Benson et al. 2003). hot gas (T > 3 × 105 K) in the disc when including runaway stars
(71% vs. 54%). We find that the opposite is true for the halo, where
the dense clouds expelled by the strong winds somewhat reduce the
5.2 Comparison to other work volume filling factor in hot gas.
The literature on galaxy scale simulations including runaway stars For our model we account for the entire galactic disc, although
is limited due to the high computational cost of treating individual this imposes constraints on the spatial resolution we can afford.
stars. Previous studies have therefore used alternative methods to As was pointed out by Martizzi et al. (2016), not accounting for
overcome this challenge. Simulations of vertically stratified patches the global geometry of the disc, as is the case for ISM patches,
of discs have been used to compare clustered and random place- leads to unreliable wind properties due to incorrect treatment of the
ment of SNe (see e.g. Korpi et al. 1999; de Avillez 2000; de Avillez gravitational potential and the disc rotation.
& Breitschwerdt 2004, 2005; Joung & Mac Low 2006; Walch et al. To our knowledge, no other simulation work of entire disc
2015; Martizzi et al. 2016; Girichidis et al. 2016; Gatto et al. 2017). galaxies have included treatment of individual runaway stars, al-
MNRAS 000, 1–14 (2020)10 E. P. Andersson et al.
though alternative methods have been studied. A model by Cev-
erino & Klypin (2009), also used in simulations by Ceverino et al.
(2014) and Zolotov et al. (2015), includes the effect of runaway
stars by applying velocity kicks to 10 − 30% of all stellar particles
101
(with masses > 104 M ) representing entire stellar populations
rather than individual massive stars. Ceverino et al. (2014) showed 100 5 kpc
that their model depend strongly on resolution with its effect dis-
50 kpc
appearing at low-resolution (60 pc) compared to high-resolution
(14 pc) simulations. This is not unexpected since the mean travel
10 1
100 kpc
distance of OB runaway stars is of order 100 pc (see Section 2.2) Bouché et al. (2012)
which sets a characteristic scale that needs to be resolved for these 10 2
Chisholm et al. (2017)
stars to differ from massive stars remaining in their natal regions. Schroetter et al. (2019)
In order to alleviate the computational expense required by
tracing the trajectory of individual stars, an intermediate step could
10 3
7 8 9 10 11
be to distribute SNe explosions around their natal stellar popula-
tion. Tress et al. (2019) used this approach by injecting SNe energy
log(M [M ])
at locations randomly sampled from a 5 pc Gaussian distribution.
Although this captures some aspects like the spatial extent of star
clusters, this is not representative of runaway stars which can travel Figure 9. Mass loading factor as function of stellar mass comparing
the results of our simulations to values observed. Our simulations, with
significantly further and yield more complex distance distributions.
runaways in red and no runaways in blue, are shown measured at three
different vertical heights (see Figure 5 for details). Orange markers show
data for galaxies at redshift ∼ 0.1 from Bouché et al. (2012). Black dia-
5.3 Comparisons to observations monds shows data from nearby star-forming galaxies from Chisholm et al.
(2017) with mass loading estimates computed from maximum outflow rates
Observational evidence for strong galactic winds is today ubiqui- divided by star formation rates derived from UV spectra. The scaling rela-
tous e.g. in starburst galaxies (Veilleux et al. 2005; Rupke 2018). tion derived in their work is shown as the dashed black line. The green
In this section we discuss how our simulations compare with the crosses shows measurements from galaxies at redshift ∼ 0.1 by Schroet-
current observational data. We note that this comparison should be ter et al. (2019). Although η depends strongly on the where outflows are
measured the ratio between the two simulations remain the same.
treated with caution since our simulations are idealised, isolated
disc galaxies without their cosmological environment.
Mass loading factors in external galaxies have been observed
to depend on galaxy mass although there is a considerable spread runaway stars as our no runaways simulation also produce low,
with mass loading factors ranging between η ∼ 0.01 − 10, even at albeit non-zero, mass loading factors.
a fixed stellar mass (Martin 1999; Bouché et al. 2012; Chisholm Another striking effect of the runaway stars is the more struc-
et al. 2017; Schroetter et al. 2019). Mass loading factors are diffi- tured and extended gas halo. The CGM is indeed observed to be
cult to extract from observations due the incomplete census of vari- highly structured (e.g. Werk et al. 2014, and references therein),
ous gas phases as well as their sensitivity to where in the galaxy one with stellar feedback leaving a specific imprint on the properties
measures them. Since observations typically use quasars absorption of the circumgalactic gaseous haloes (e.g. Liang et al. 2016). To
spectra to study winds in external galaxies the random positioning date, no consensus exists on what is driving the fine scale structure
of the quasar with respect to star forming galaxies makes this a of the CGM, partly due to the fact that galaxy scale simulations
challenging endeavour. In Figure 9 we show a composite of obser- are far from resolving the (likely) parsec scale clouds that make up
vationally derived mass loading factors as function of stellar mass the halo on small scales (see discussion in Section 5.5). We leave
including a fit from Chisholm et al. (2017) together with our results. a study of the impact of run-away stars on halo absorber column
The data indicates a negative trend with stellar mass, as well as a density profiles and covering fractions for a future study.
large scatter. We show the final values of our results at three differ- In Section 4.3 we noted that more halo gas clouds existed
ent heights above the disc plane. These values are in broad agree- across a wide range of temperatures in the runaways simulation.
ment with the entire spread in the observations, with the exception They arise from gas lifted from the disc as well as halo gas com-
of the outermost measurements of the no runaways simulation. pression from self-gravity followed by efficient cooling (indeed,
This implies that the spread in our simulations is due to either: cooling is most efficient at T ∼ few × 105 K, with feedback driven
1) height above the disc plane; 2) the different stellar physics we perturbations leading to thermal instabilities Joung et al. (2012) and
consider, i.e., runaway stars. In the absence of information on the cloud formation). In reality, these clouds may be destroyed via hy-
height of measurements (due to uncertain inclination of the disc) it drodynamical instabilities as they fall back onto the disc (Heitsch &
is not possible to disentangle these two possibilities. Putman 2009), a process that is likely not fully captured in our mod-
Other simulation work have modelled self-consistent driving els. Regardless, these clouds could be interpreted as high velocity
of galactic outflows from stellar feedback in massive galaxies. No- clouds (HVC), which are observed in the Milky Way halo (Blitz
tably, Muratov et al. (2015) analysed the FIRE simulation suite and et al. 1999; Wakker 2004; Moss et al. 2013, 2017). The origin of
found that for M? & 1010 M , mass loading factors were consis- the HVCs is still an open question (Lockman et al. 2019), and al-
tent with η ∼ 0 when measured at 0.25Rvir ≈ 50 kpc (see their though the most distant ones are likely from cosmic origin (see e.g.,
figure 6). This is incompatible with the observations compiled in Richter 2012), there are plenty of clouds observed within few tens
Figure 9, and illustrates that the role of stellar feedback driven of kpc (see Wakker et al. 2008), compatible with our runaways
winds in galaxies of this mass is not yet understood. The results model. It is likely that at least some fraction of these clouds origi-
of Muratov et al. may indicate a lack of additional physics such as nate from outflows (Quilis & Moore 2001), making the more effi-
MNRAS 000, 1–14 (2020)Increased outflows with runaways 11
runaways no runaways
300
0
[M yr 1 kpc 2])
250
200
vp [km s 1]
2
150
4 100
SFR
6 50
log(
2 1 0 1 2 1 0 1 2 0
log( g [M pc 2]) log( g [M pc 2])
Figure 10. Resolved Kennicutt-Schmidt relation, ΣSFR versus Σg , comparing the runaway model (left) to the model ignoring runaway stars (right). Each point
is a measurement from a 1 kpc square in the 24 kpc wide face-on view of the galaxy using data from our last output. To compute the star formation rate we
use an age bin of 2 Myr. The colours show the mean velocity of all these stars, calculated after removing the velocity component coming from the rotational
velocity. The grey dashed line shows the empirical relation fitted by Daddi et al. (2010) for disc galaxies. The runaways simulation includes a group of
points with star formation rates ∼ 10−5 M yr−1 kpc−2 which corresponds to runaway stars, as is indicated by the high velocity of the stars in these points.
cient coupling of feedback energy to the galactic halo allowed by The first consists of a galaxy formed from collapsing gas in an
runaway stars an interesting addition to the formation scenario of analytical description of a dark matter halo. Its potential is set
HVCs. up according to a Navarro-Frenk-White (NFW) profile (Navarro
Finally, we briefly highlight a curious effect found when in- et al. 1997) with R200 = 50 kpc, where the rotational velocity is
cluding runaway stars in our simulations, namely their effect on the 35 km s−1 . This setup is identical to that of Teyssier et al. (2013),
resolved Kennicutt-Schmidt (KS) relation. This relation is shown except they used a “live" halo described by particles. We adopt the
for the final output of both the runaways and no runaways sim- same star formation and feedback recipes as is described in Sec-
ulation in Figure 10, together with the relation from Daddi et al. tion 2 and compared the evolution of one with and one without our
(2010) (see also Kennicutt 1998). With runaways we find re- runaway star model. After a settling phase the star formation and
gions of the disc which reside significantly below the canonical outflow rates were almost identical regardless of whether runaway
value, reaching ΣSFR ∼ 10−6 M yr−1 kpc−2 . Since our model stars are included or not. In addition to the isolated dwarf galaxy
has a finite mass resolution for star formation events (∼ 500 M ), we simulated the formation of a ultra faint dwarf (UFD) galaxy
a lower limit to star formation surface densities of ΣSFR ≈ (M200 = 109 M at z = 0) in cosmological setting. The setup used
10−4 M yr−1 kpc−2 , for the accounted time (2 Myr) and area is the same as the fiducial simulation in Agertz et al. (2020), except
(1 kpc2 ), is expected. This is indeed the case for no runaways, that we include our star formation and feedback models. Akin to
since stars does not significantly change in mass over 2 Myr. In the isolated dwarf galaxy we find a surprisingly small effect when
contrast, in the runaways model this is enough for a fraction of including runaway stars, despite the mean travel distance for SNe
runaway stars to venture away from their natal region and masquer- progenitors being on the order of the half mass radius (∼ 300 pc)
ade as inefficient star formation events. This is highlighted by the of the simulated UFD.
deviation in mean peculiar velocity of the stars shown by colour We attribute the lack of impact of runaways on dwarf galaxies,
in Figure 10. Runaway star may therefore provide an explanation at least in terms of outflow properties, to the high porosity of the
for the extremely inefficient star formation observed in local spiral ISM which arises due to the shallow potential. This implies that
and dwarf galaxies (Bigiel et al. 2010) which we will focus on in energy from any SN is likely to efficiently couple to diffuse gas
forthcoming work (Andersson et al., in prep.) within or outside galaxy, regardless of the inclusion of runaways.
Nonetheless, since runaway stars can leave the galaxy entirely one
may expect a different enrichment history for the CGM. How this
5.4 The impact of runaway stars in dwarf galaxies affects the chemistry of the dwarf galaxy and its environment in the
long term deserves a dedicated study.
Dwarf galaxies have shallow potential wells and are expected to
be strongly affected by stellar feedback, with higher mass loading
factors than the cases studied here (see Figure 9) resulting in low
5.5 Limitations of the model
galaxy formation efficiencies (Behroozi et al. 2019).
To give us an indication of how runaway stars impact these Throughout this work we have outlined limitations to our model.
low mass galaxies we set up two additional pairs of simulations. In this section we summarise these points, and discuss possible im-
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